18 1 Lect-18 In this lecture ... • Stirling and Ericsson cycles • Brayton cycle: The ideal cycle for gas- turbine engines • The Brayton cycle with regeneration • The Brayton cycle with intercooling, reheating and regeneration • Rankine cycle: The ideal cycle for vapour power cycles 2 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Stirling and Ericsson cycles • The ideal Otto and Diesel cycles are internally reversible, but not totally reversible. • Hence their efficiencies will always be less than that of Carnot efficiency. • For a cycle to approach a Carnot cycle, heat addition and heat rejection must take place isothermally. • Stirling and Ericsson cycles comprise of isothermal heat addition and heat rejection. 3 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Regeneration Working fluid • Both these cycles also have a regeneration process. • Regeneration, a process during which heat is Energy transferred to a thermal energy storage device Energy (called a regenerator) during one part of the cycle and is transferred back to the working fluid during Concept of a regenerator another part of the cycle. 4 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Stirling cycle • Consists of four totally reversible processes: – 1-2 T = constant, expansion (heat addition from the external source) – 2-3 v = constant, regeneration (internal heat transfer from the working fluid to the regenerator) – 3-4 T= constant, compression (heat rejection to the external sink) – 4-1 v = constant, regeneration (internal heat transfer from the regenerator back to the working fluid) 5 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-17 Stirling cycle P 1 T qin qin Regeneration Isothermal 1 2 Isochoric 4 2 4 3 qout qout 3 v s Stirling cycle on P-v and T-s diagrams 6 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Ericsson cycle • Consists of four totally reversible processes: – 1-2 T = constant, expansion (heat addition from the external source) – 2-3 P = constant, regeneration (internal heat transfer from the working fluid to the regenerator) – 3-4 T= constant, compression (heat rejection to the external sink) – 4-1 P = constant, regeneration (internal heat transfer from the regenerator back to the working fluid) 7 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-17 Ericsson cycle Isothermal P 1 T 4 Regeneration qin 1 2 qin Isobaric qout 4 3 3 2 q Regeneration out v s Ericsson cycle on P-v and T-s diagrams 8 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Stirling and Ericsson cycles • Since both these engines are totally reversible cycles, their efficiencies equal the Carnot efficiency between same temperature limits. • These cycles are difficult to realise practically, but offer great potential. • Regeneration increases efficiency. • This fact is used in many modern day cycles to improve efficiency. 9 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle • The Brayton cycle was proposed by George Brayton in 1870 for use in reciprocating engines. • Modern day gas turbines operate on Brayton cycle and work with rotating machinery. • Gas turbines operate in open-cycle mode, but can be modelled as closed cycle using air- standard assumptions. • Combustion and exhaust replaced by constant pressure heat addition and rejection. 10 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle • The Brayton cycle consists of four internally reversible processes: – 1-2 Isentropic compression (in a compressor) – 2-3 Constant-pressure heat addition – 3-4 Isentropic expansion (in a turbine) – 4-1 Constant-pressure heat rejection 11 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle q 3 in Isentropic Isobaric P 3 T 2 qin 2 4 qout 1 4 1 qout v s Brayton cycle on P-v and T-s diagrams 12 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle • The energy balance for a steady-flow process can be expressed as: (qin − qout ) + (win − wout ) = ∆h The heat transfer to and from the working fluid can be written as : qin = h3 − h2 = c p (T3 −T2 ) qout = h4 − h1 = c p (T4 −T1) 13 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle • The thermal efficiency of the ideal Brayton cycle under the cold air standard assumptions becomes: wnet qout T4 −T1 T1(T4 /T1 −1) ηth,Brayton = =1− =1− =1− qin qin T3 −T2 T2 (T3 /T2 −1) Processes 1- 2 and 3- 4 are isentropic and P2 = P3 and P4 = P1. (γ −1)/γ (γ −1)/γ T1 P2 P3 T3 Therefore, = = = T2 P1 P4 T4 14 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle • Substituting these equations into the thermal efficiency relation and simplifying: 1 ηth,Brayton =1− (γ −1)/γ rp P2 where, rp = is the pressure ratio. P1 • The thermal efficiency of a Brayton cycle is therefore a function of the cycle pressure ratio and the ratio of specific heats. 15 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle with regeneration • Regeneration can be carried out by using the hot air exhausting from the turbine to heat up the compressor exit flow. • The thermal efficiency of the Brayton cycle increases as a part of the heat rejected is re- used. • Regeneration decreases the heat input (thus fuel) requirements for the same net work output. 16 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle with regeneration 3 qin T qregen 5’ 4 5 Regeneration 2 6 qsaved=qregen 1 qout s T-s diagram of a Brayton cycle with regeneration 17 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle with regeneration • The highest temperature occurring within the regenerator is T4. • Air normally leaves the regenerator at a lower temperature, T5. • In the limiting (ideal) case, the air exits the regenerator at the inlet temperature of the exhaust gases T4. • The actual and maximum heat transfers are: qregen,act = h5 - h2 and qregen,max = h5’- h2 = h4 - h2 18 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle with regeneration • The extent to which a regenerator approaches an ideal regenerator is called the effectiveness, ε and is defined as ε = qregen,act / qregen,max = (h5 - h2)/(h4 - h2) • Under the cold-air-standard assumptions, the thermal efficiency of an ideal Brayton cycle with regeneration is: T η = − 1 (γ −1)/γ th,regen 1 (rp ) T3 • The thermal efficiency depends upon the temperature as well as the pressure ratio. 19 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle with intercooling, reheating and regeneration • The net work of a gas-turbine cycle is the difference between the turbine work output and the compressor work input. • It can be increased by either decreasing the compressor work or increasing the turbine work, or both. • The work required to compress a gas between two specified pressures can be decreased by carrying out the compression process in stages and cooling the gas in between: multi-stage compression with intercooling. 20 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle with intercooling, reheating and regeneration • Similarly the work output of a turbine can be increased by: multi-stage expansion with reheating. • As the number of stages of compression and expansion are increased, the process approaches an isothermal process. • A combination of intercooling and reheating can increase the net work output of a Brayton cycle significantly. 21 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle with intercooling, reheating and regeneration Polytropic process paths P D C Work saved as a result of intercooling B A Intercooling Isothermal process path 1 v Work inputs to a single-stage compressor (process: 1AC) and a two-stage compressor with intercooling (process: 1ABD). 22 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle with intercooling, reheating and regeneration 6 8 q T in qregen 5 9 7 4 2 10 qsaved=qregen 3 1 qout s T-s diagram of an ideal gas-turbine cycle with intercooling, reheating, and regeneration 23 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle with intercooling, reheating and regeneration • The net work output of a gas-turbine cycle improves as a result of intercooling and reheating. • However, intercooling and reheating decreases the thermal efficiency unless they are accompanied by regeneration. • This is because intercooling decreases the average temperature at which heat is added, and reheating increases the average temperature at which heat is rejected. 24 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Brayton cycle with intercooling, reheating and regeneration T TH,avg P=const TL,avg s As the number of compression and expansion stages increases, the Brayton cycle with intercooling, reheating, and regeneration approaches the Ericsson cycle. 25 Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay Lect-18 Rankine cycle • Rankine cycle is the ideal cycle for vapour power cycles. • The ideal Rankine cycle does not involve any internal irreversibilities. • The ideal cycle consists of the following: – 1-2 Isentropic compression in a pump – 2-3 Constant pressure heat addition in a boiler – 3-4 Isentropic expansion in a turbine – 4-1 Constant pressure heat rejection in a condenser 26 Prof.